Brillouin–Wigner perturbation theory

E33422

perturbation theory quantum mechanical formalism

Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.

Aliases (2)

Statements (41)

Predicate	Object
instanceOf	perturbation theory → quantum mechanical formalism →
advantage	can improve convergence of perturbation series in some problems →
aimsTo	obtain improved approximations to eigenstates → obtain improved approximations to eigenvalues →
appliedIn	nuclear shell-model calculations →
appliesTo	discrete spectra → time-independent Hamiltonians →
assumes	existence of a solvable unperturbed Hamiltonian →
basedOn	partition of Hamiltonian into unperturbed and perturbation parts →
category	approximation method in quantum theory →
characteristic	energy appearing on both sides of the eigenvalue equation →
comparedTo	Rayleigh–Schrödinger perturbation theory →
contrastWith	Rayleigh–Schrödinger perturbation theory using energy-independent effective Hamiltonian →
developedIn	20th century →
feature	nonlinear dependence of energy corrections on the exact energy →
field	quantum mechanics →
focusesOn	corrections to eigenvalues and eigenvectors of the unperturbed Hamiltonian →
formalismType	time-independent perturbation theory →
framework	Hilbert space of quantum states →
goal	improve accuracy beyond low-order perturbation results →
involves	projection operators onto model space and complementary space →
limitation	leads to implicit equations for energies → requires self-consistent solution for eigenvalues →
mathematicalForm	series expansion in powers of the perturbation →
namedAfter	Eugene Wigner → Léon Brillouin →
relatedConcept	Brillouin–Wigner expansion → quasi-degenerate perturbation theory →
relatedTo	Feshbach projection formalism → effective Hamiltonian methods →
requires	choice of model space → definition of projection operators →
usedFor	bound-state problems in quantum mechanics → many-body quantum systems →
usedIn	atomic physics → condensed matter physics → molecular physics →
usedToDerive	effective interactions in model spaces →
uses	energy-dependent effective Hamiltonian →
yields	energy-dependent effective Hamiltonian in model space →

Referenced by (3)

Subject (surface form when different)	Predicate
Brillouin–Wigner perturbation theory ("quasi-degenerate perturbation theory") → Brillouin–Wigner perturbation theory ("Brillouin–Wigner expansion") →	relatedConcept
Rayleigh–Schrödinger perturbation theory →	relatedTo